I am in need of recommendations for a history of 20C mathematics, esp from
Hilbert through Gödel to Turing and von Neumann; it would also be useful to
read about how Mr Turing's machine (as Richard Feynman calls it) has
affected mathematics since. I'm interested in a philosophical view of this
history, but it's important to me to get the facts straight, e.g. which
important papers were published when. I'd like to understand which of
Hilbert's famous problems proved important to this particular history and
why. At the same time I'd rejoice in a view sufficiently strong to risk a
few sentences that sum up the gist of how Hilbert's project ran aground,
why and what this tells us about computing. Constance Reid's Hilbert is, as
she says, more of a poetic celebration of mathematics (and German academic
culture of the period) than a real history; frustratingly it gives few
references, for example. I need a more scholarly poem!